In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences Jintroduced there is unusable for such sums and consequently the results obt...In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences Jintroduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class Jusable considering a particular double cosine trigonometric series.展开更多
We study here Ll-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for Ll-cOnvergence of double cosine trigonometric series. Also, the results obtained by ...We study here Ll-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for Ll-cOnvergence of double cosine trigonometric series. Also, the results obtained by Moricz[1],[2] are particular cases of ours.展开更多
In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for th...In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L^1 convergence are given for the process with the suitably normed condition.展开更多
文摘In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences Jintroduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class Jusable considering a particular double cosine trigonometric series.
文摘We study here Ll-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for Ll-cOnvergence of double cosine trigonometric series. Also, the results obtained by Moricz[1],[2] are particular cases of ours.
文摘In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L^1 convergence are given for the process with the suitably normed condition.
